Numerical simulation of a hyperbolic model for chemotaxis after blow up
Résumé
A macroscopic system modelling the chemotactic motion of bacteria is considered. This model has been obtained in a previous work thanks to a hydrodynamical limit of a kinetic system. Existence and uniqueness of measure solutions for this system using the concept of duality solution have been proved by the authors in \cite{jamesnv}. In this paper, we investigate the numerical discretization of this system. A scheme based on a finite volume approach is proposed and the convergence of the numerical solution towards the unique duality solution is stated. Numerical simulations are provided that shows the behaviour of solutions after blow up.
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